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The original MRF optimization problem is NP-hard and we need to transform it into something easier. is a set of sub-trees of graph where its trees cover all nodes and edges of the main graph. And MRFs defined for every tree in will be smaller.
In the domain of physics and probability, a Markov random field (MRF), Markov network or undirected graphical model is a set of random variables having a Markov property described by an undirected graph. In other words, a random field is said to be a Markov random field if it satisfies Markov properties.
Magnetic resonance fingerprinting (MRF) is methodology in quantitative magnetic resonance imaging (MRI) characterized by a pseudo-randomized acquisition strategy. It involves creating unique signal patterns or 'fingerprints' for different materials or tissues after which a pattern recognition algorithm matches these fingerprints with a predefined dictionary of expected signal patterns.
Data science is multifaceted and can be described as a science, a research paradigm, a research method, a discipline, a workflow, and a profession. [4] Data science is "a concept to unify statistics, data analysis, informatics, and their related methods" to "understand and analyze actual phenomena" with data. [5]
M. Kearns, U. Vazirani. An Introduction to Computational Learning Theory. MIT Press, 1994. A textbook. M. Mohri, A. Rostamizadeh, and A. Talwalkar.
Computational statistics, or statistical computing, is the study which is the intersection of statistics and computer science, and refers to the statistical methods that are enabled by using computational methods. It is the area of computational science (or scientific computing) specific to the mathematical science of statistics. This area is ...
Randomization is a statistical process in which a random mechanism is employed to select a sample from a population or assign subjects to different groups. [1] [2] [3] The process is crucial in ensuring the random allocation of experimental units or treatment protocols, thereby minimizing selection bias and enhancing the statistical validity. [4]
The CD index for papers published in Nature, PNAS, and Science and Nobel-Prize-winning papers [83] The CD index may indicate a "decline of disruptive science and technology". [83] Metascience research is investigating the growth of science overall, using e.g. data on the number of publications in bibliographic databases. A study found segments ...